Virtual element approximation of eigenvalue problems
Daniele Boffi, Francesca Gardini, Lucia Gastaldi
TL;DR
This paper explores the virtual element method for approximating eigenvalues in elliptic PDEs, detailing the theoretical framework, implementation features, and practical applications.
Contribution
It provides a comprehensive analysis of the virtual element method for eigenvalue problems, including stability and application insights.
Findings
Effective approximation of eigenvalues demonstrated
Impact of stabilizing parameters analyzed
Application examples showcase method versatility
Abstract
We discuss the approximation of eigenvalue problems associated with elliptic partial differential equations using the virtual element method. After recalling the abstract theory, we present a model problem, describing in detail the features of the scheme, and highligting the effects of the stabilizing parameters. We conlcude the discussion with a survey of several application examples.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Numerical methods in engineering · Advanced Mathematical Modeling in Engineering